Most terms in (REF ) are total divergence terms, integrating to zero, or vanish due to Maxwell's equations in vacuum. Therefore essentially we have the well-known [1]}, [2]} results,
\(J^\mu = a^\nu P^{\mu }_{\,\nu } + \frac{1}{2}\,R^{\alpha \beta }\,M_{\beta \alpha }^\mu + F^{\mu \nu }\tilde{A}_\nu - \tilde{F}^{\mu \nu }\,A_\nu \,,\) 
